- Introduction I. Fed’s Stock Valuation Model
How can we judge whether stock prices are too high, too low, or just right? The purpose of
this weekly report is to track a stock valuation model that attempts to answer this question.
While the model is very simple, it has been quite accurate and can also be used as a stocksversus-bonds asset allocation tool. I started to study the model in 1997, after reading that the
folks at the Federal Reserve have been using it. If it is good enough for them, it’s good
enough for me. I dubbed it the Fed’s Stock Valuation Model (FSVM), though no one at the
Fed ever officially endorsed it.
On December 5, 1996, Alan Greenspan, Chairman of the Federal Reserve Board, famously
worried out loud for the first time about “irrational exuberance” in the stock market. He
didn’t actually say that stock prices were too high. Rather he asked the question: “But how
do we know when irrational exuberance has unduly escalated asset values, which then
become subject to unexpected and prolonged contractions….”1 He did it again on February
26, 1997.2 He probably instructed his staff to devise a stock market valuation model to help
him evaluate the extent of the market’s exuberance. Apparently, they did so and it was made
public, though buried, in the Fed’s Monetary Policy Report to the Congress, which
accompanied Mr. Greenspan’s Humphrey-Hawkins testimony on July 22, 1997.3
The Fed model was summed up in one paragraph and one chart on page 24 of the 25-page
document (see following table). The chart shows a strong correlation between the S&P 500
forward earnings yield (FEY)—i.e., the ratio of expected operating earnings (E) to the
price index for the S&P 500 companies (P), using 12-month-ahead consensus earnings
estimates compiled by Thomson Financial First Call.—and the 10-year Treasury bond
yield (TBY). The average spread between the forward earnings yield and the Treasury
yield (i.e., FEY-TBY) is 29 basis points since 1979. This near-zero average implies that
the market is fairly valued when the two are identical:
1)

FEY = TBY

Of course, in the investment community, we tend to follow the price-to-earnings ratio more
than the earnings yield. The ratio of the S&P 500 price index to expected earnings (P/E) is
highly correlated with the reciprocal of the 10-year bond yield, and on average the two
have been nearly identical. In other words, the “fair value” price for the S&P 500 (FVP) is
equal to expected earnings divided by the bond yield in the Fed’s valuation model:

1

http://www.federalreserve.gov/boarddocs/speeches/1996/19961205.htm
“We have not been able, as yet, to provide a satisfying answer to this question, but there are reasons in the
current environment to keep this question on the table.”
http://www.federalreserve.gov/boarddocs/hh/1997/february/testimony.htm
3
http://www.federalreserve.gov/boarddocs/hh/1997/july/ReportSection2.htm
2

Excerpt from Fed’s July 1997 Monetary Policy Report:
The run-up in stock prices in the spring was bolstered by unexpectedly strong
corporate profits for the first quarter. Still, the ratio of prices in the S&P 500 to
consensus estimates of earnings over the coming twelve months has risen further from
levels that were already unusually high. Changes in this ratio have often been inversely
related to changes in long-term Treasury yields, but this year’s stock price gains were
not matched by a significant net decline in interest rates. As a result, the yield on tenyear Treasury notes now exceeds the ratio of twelve-month-ahead earnings to prices
by the largest amount since 1991, when earnings were depressed by the economic
slowdown. One important factor behind the increase in stock prices this year appears
to be a further rise in analysts’ reported expectations of earnings growth over the next
three to five years. The average of these expectations has risen fairly steadily since
early 1995 and currently stands at a level not seen since the steep recession of the
early 1980s, when earnings were expected to bounce back from levels that were quite
low.

The ratio of the actual S&P 500 price index to the fair value price shows the degree of
overvaluation or undervaluation. History shows that markets can stay overvalued and
become even more overvalued for a while. But eventually, overvaluation is corrected in
three ways: 1) falling interest rates, 2) higher earnings expectations, and of course, 3)
falling stock prices—the old fashioned way to decrease values. Undervaluation can be
corrected by rising yields, lower earnings expectations, or higher stock prices.
The Fed’s Stock Valuation Model worked quite well in the past. It identified when stock
prices were excessively overvalued or undervalued, and likely to fall or rise:
1) The market was extremely undervalued from 1979 through 1982, setting the stage for a
powerful rally that lasted through the summer of 1987.
2) Stock prices crashed after the market rose to a record 34% overvaluation peak during
September 1987.
3) Then the market was undervalued in the late 1980s, and stock prices rose.
4) In the early 1990s, it was moderately overvalued and stock values advanced at a
lackluster pace.
5) Stock prices were mostly undervalued during the mid-1990s, and a great bull market
started in late 1994.
6) Ironically, the market was actually fairly valued during December 1996 when the Fed
Chairman worried out loud about irrational exuberance.
Deutsche Banc Alex. Brown US Stock Valuation & Allocation Models / August 13, 2001 / Page 3

7) During both the summers of 1997 and 1998, overvaluation conditions were corrected
by a sharp drop in prices.
8) Then a two-month undervaluation condition during September and October 1998 was
quickly reversed as stock prices soared to a remarkable record 70% overvaluation
reading during January 2000. This bubble was led by the Nasdaq and technology
stocks, which crashed over the rest of the year, bringing the market closer to fair value.

II. New Improved Model
The FSVM is missing a variable reflecting that the forward earnings yield is riskier than
the government bond yield. How should we measure risk in the model? An obvious choice
is to use the spread between corporate bond yields and Treasury bond yields. This spread
measures the market’s assessment of the risk that some corporations might be forced to
default on their bonds. Of course, such events are very unusual, especially for companies
included in the S&P 500. However, the spread is only likely to widen during periods of
economic distress, when bond investors tend to worry that profits won’t be sufficient to
meet the debt-servicing obligations of some companies. Most companies won’t have this
problem, but their earnings would most likely be depressed during such periods. The
FSVM is also missing a variable for long-term earnings growth. My New Improved Model
includes these variables as follows:
3)

FEY = CBY – b • LTEG

where CBY is Moody’s A-rated corporate bond yield. LTEG is long-term expected
earnings growth, which is measured using consensus five-year earnings growth
projections. I/B/E/S International compiles these monthly. The “b” coefficient is the
weight that the market gives to long-term earnings projections. It can be derived as -[FEYCBY]/LTEG. Since the start of the data in 1985, this “earnings growth coefficient”
averaged 0.1.
Equation 3 can be rearranged to produce the following:
4)

FVP = E ÷ [CBY – b • LTEG]

FVP is the fair value price of the S&P 500 index. Exhibit 10 shows three fair value price
series using the actual data for E, CBY, and LTEG with b = 0.1, b = 0.2, and b = 0.25. The
market was fairly valued during 1999 and the first half of 2000 based on the consensus
forecast that earnings could grow more than 16% per year over the next five years and that
this variable should be weighted by 0.25, or two and a half times more than the average
historical weight.

III. Back To Basics
With the benefit of hindsight, it seems that these assumptions were too optimistic. But, this
is exactly the added value of the New Improved FSVM. It can be used to make explicit the
Page 4 / August 13, 2001 / Deutsche Banc Alex. Brown US Stock Valuation & Allocation Models

implicit assumptions in the stock market about the weight given to long-term earnings
growth. The simple version has worked so well historically because the long-term growth
component has been offset on average by the risk variable in the corporate bond market.

IV. Stocks Versus Bonds
The FSVM is a very simple stock valuation model. It should be used along with other
stock valuation tools, including the New Improved version of the model. Of course, there
are numerous other more sophisticated and complex models. The Fed model is not a
market-timing tool. As noted above, an overvalued (undervalued) market can become even
more overvalued (undervalued). However, the Fed model does have a good track record of
showing whether stocks are cheap or expensive. Investors are likely to earn below (above)
average returns over the next 12-24 months when the market is overvalued (undervalued).
The next logical step is to convert the FSVM into a simple asset allocation model (Exhibit 1
on front cover). Iâ&#x20AC;&#x2122;ve done so by subjectively associating the â&#x20AC;&#x153;rightâ&#x20AC;? stock/bond asset mixes
with the degree of over/under valuation as shown in the table below. For example, whenever
stocks are 10% to 20% overvalued, I would recommend that a large institutional equity
portfolio should have a mix with 70% in stocks and 30% in bonds.

This chart appeared
in the Fedâ&#x20AC;&#x2122;s July
1997 Monetary
Policy Report to the
Congress. It shows
a very close
correlation between
the earnings yield of
the stock market
and the bond yield.
Another, more
familiar way to look
at it follows.

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